This work introduces a semi-analytical formulation for the simulation and modeling of curved structures based on the scaled boundary finite element method (SBFEM). This approach adapts the fundamental idea of the SBFEM concept to scale a boundary to describe a geometry. Until now, scaling in SBFEM has exclusively been performed along a straight coordinate that enlarges, shrinks, or shifts a given boundary. In this novel approach, scaling is based on a polar or cylindrical coordinate system such that a boundary is shifted along a curved scaling direction. The derived formulations are used to compute the static and dynamic stiffness matrices of homogeneous curved structures. The resulting elements can be coupled to general SBFEM or FEM domains. For elastodynamic problems, computations are performed in the frequency domain. Results of this work are validated using the global matrix method and standard finite element analysis.

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This contribution presents the study of strange phenomena in wave mode representations of waveguides. For this study the waveguides are computed by means of the Scaled Boundary Finite Element Method (SBFEM). Different approaches of mode tracing are used to identify the characteristics of the resulting wave modes. Higher order differentials of the underlying eigenvalue problem are the basis for these approaches. The main idea behind this mode tracing approach is to reduce the cubic computation time to solve the eigenvalue problem for each frequency of interest. This study identifies potentially critical frequency regions and attempts to formulate a solution process. The fascinating effects at critical frequencies are displayed and a suggestion for a stabilization for the solution process is made. This study bases its conclusion on a numerical viewpoint. Main aspects in this study include high order differentials of the eigenvalue problem and the corresponding Taylor and Padé approximations for the eigenvalue problem as a whole. Simulation of elastic guided waves is an essential tool for a number of important applications. Especially the field of nondestructive testing (NDT) with ultrasonic waves needs precise descriptions of wave propagation -often in form of dispersion curves. Analytical approaches like [1] can compute dispersion curves for specific geometries, but are strictly limited to these. While standard FEM simulation can deal with more complex problems in theory, three specific aspects increase computation requirements beyond acceptable limits. Firstly the ultrasonic frequency range deals with very small wavelengths and therefore requires fine meshing. Secondly geometries can be very large with high complexity and therefore increase the general mesh dimensions. Thirdly certain methods in NDT solve inverse problems and therefore have to be simulated many times. Consequently simulations have to be performed with tools adapted to the problem. This paper is based on the semi-analytical Scaled Boundary Finite Element Method (SBFEM). The SBFEM reduces computational time significantly by meshing the boundary only and applying an analytical solution in the interior of the domain. The formulations in [4] use SBFEM to describe wave propagation in waveguides of constant cross-section. Solution for wave numbers k and the corresponding displacement field ψ on the boundary are computed by solving an eigenvalue problem:for any angular frequency ω. The Matrices E 0 , E 1 , E 2 , M 0 describe the meshed surface. Dispersion curves, showing the frequency-wave number correlation, are therefore derived by solving the eigenvalue problem at each frequency of interest.The idea of this work is to solve the eigenvalue problem once and then apply approximations for extended frequency ranges like [2]. Several approaches show great performances for a variety of cases, but under certain unfavorable circumstances most methods run into problems -mainly expressed in the loss of solutions or producing a small number of wrong solutions. L...